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中文論文名稱 關於導數為有界的函數的Hermite-Hadamard型不等式的研究
英文論文名稱 Inequalities of Hermite-Hadamard type for functions whose derivatives in absolute values are quasi-convex
校院名稱 淡江大學
系所名稱(中) 中等學校教師在職進修數學教學碩士學位班
系所名稱(英) Executive Master's Program In Mathematics for Teachers
學年度 100
學期 2
出版年 101
研究生中文姓名 謝瑾瑜
研究生英文姓名 Chin-Yu Hsieh
學號 799190078
學位類別 碩士
語文別 中文
第二語文別 英文
口試日期 2012-06-09
論文頁數 53頁
口試委員 指導教授-楊國勝
委員-李武炎
委員-曾貴麟
中文關鍵字 Hermite-Hadamard 不等式  準凸函數 
英文關鍵字 Hermite-Hadamard inequality  Quasi-convex function. 
學科別分類
中文摘要 本研究的主要目的為建立有關導數為有界且為準凸函數(quasi-convex function)的 Hermite-Hadamard 不等式之推廣,以及估計一般化的中點公式誤差的界限。所得到的研究結果可應用於藉由中點公式去估計積分之近似誤差。
英文摘要 The main purpose of this paper is to establish some inequalities of Hermite-Hadamard type for functions whose derivatives in absolute values are quasi-convex , and some error estimates for the generalized midpoint formula . The obtained results can be used to give estimates for the approximation error of the integral by the use of the midpoint formula .
論文目次 中文摘要 i
英文摘要 ii
目 次 iii
一、 前言 1
二、 主要的結果 5
三、 中點公式之應用 19
參考文獻 25
附錄
1. Introduction 27
2. Main results 31
3. Applications to the midpoint formula 46
References 52
參考文獻 [1] M , Alomari , M.Darus , and S.S. Dragomir , Inequlities of ermite-Hadamard’s
type for function , whose derivatives absolute values are quasi-convex ,
Punjab University J.Math.submitted .
[2] S.S. Dragomir , Two mappings in connection to Hadamard’s inequalities , J.
Math. Anal. Appl. , 167 (1992) , 49-56.
[3] S.S. Dragomir and R.P. Agarwal , Two inequalities for differentiable mappings
and applications to special means of real numbers and to trapezoidal formula ,
Appl. Math. Lett , 11(1998) , 91-95.
[4] S.S. Dragomir , Y.J. Cho and S.S. Kim, Inequalities of Hadamard’s type for
Lipschitzian mappings and their applications , J. Math. Anal. Appl. 245(2000) ,
489-501.
[5] S.S. Dragomir and S. Wang , A new inequality of Ostrowski’s type in
norm and applications to some special means and for some numerical
quadrature rule , Tamkang J. Math , 28(1997) , 239-244 .
[6] S.S. Dragomir and S. Wang . Applications of Ostrowski’s inequality to the
estimation of error bounds for some special means and for some numerical
quadrature rule , Appl. Math. Lett . , 11(1998) ,105-109 .
[7] D.A. Ion, Some estimates on the Hermite-Hadamard inequality through
quasi-convex functions , Annals of University of Craiova , Math. Comp. Sci.
Ser. , 34(2007) , 82-87 .
[8] U.S. Kirmaci , Inequalities for differentiable mappings and applications to
special means of real numbers to midpoint formula , Appl. Math. Comp.,
147(2004) , 137-146.
[9] U.S. Kirmaci and M.E. Ozdemir , On some inequalities for differentiable
mappings and applications to special means of real numbers and to midpoint
formula , Appl. Math. Comp. 153(2004) , 361-368 .
[10] M.E. Ozdemir , Atheorem on mappings with bounded derivatives with
applications to quadrature rules and means, Appl. Math . Comp, 138(2003) ,
425-434
[11] C.E.M. Pearce and J. Pecaric , Inequalities for differectiable mappings with
application to special means , Appl. Math. Comp. 13(2000) , 51-55.
[12] G.S. Yang , D.Y. Hwang and K.I.. Tseng , Some inequalities for differentiable
convex and concave mappings , Comp. Math. Appl. , 47(2004), 207-216.
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